In a bowl, combine the tuna, celery, parsley, pickle relish, lemon juice and mayonnaise (see note for options). Toss with a fork until well mixed.Place bread slices on a broiler pan. Divide the tuna mixture evenly, mounding slightly. Sprinkle cheddar evenly over the tuna mixture.

Place open face under broiler until cheese just begin to bubble (3 to 4 minutes), watch carefully or cheese may brown too much. If serving open face they're ready, otherwise cover with top slice of bread and place under broiler until top slices toast.